Beaconless adaptive optics system
An improved beaconless adaptive optics system and process. A target is illuminated with a high energy laser beam of a directed energy laser. Wave front measurements are made of high energy laser beam reflections from the target. These wave front measurements are analyzed by a high speed processor to determine both high frequency phase components and low frequency phase components in the wave front data. (Applicants' experiments have shown that there is a direct correlation between beam spot size on the target and the phase variance of the reflected laser beam. The correlation is: the greater the phase variance the smaller the beam spot size.) Applicants have developed a technique for providing special control algorithms that provide very high speed control of the elements of a deformable mirror using this phase variance as a feedback parameter. Applicants have also developed algorithms to correct a limited number of Zernike modes associated with the wave front control.
This application claims the benefit of provisional patent application Ser. No. 60/933,603 filed Jun. 6, 2008.
FEDERAL SPONSORED RESEARCHThe present invention was made in the course of performance of Contract Nos. FA945106D0006 and FA945104C0321 with the United States Air Force and the United States Government has rights in the invention.
FIELD OF INVENTIONThe present invention relates to imaging and laser projection systems and in particular to such systems involving turbulence.
BACKGROUND OF THE INVENTION Directed Energy SystemsSince the invention of the laser, consideration has been given to development of directed energy systems. These systems require techniques to maximize the laser power density on the target. This means the laser “spot size” on the target must be as small as possible. Recent progress in high power laser technology makes these systems feasible. However, depositing lethal flux on the target over sufficient time requires mitigation of the atmospheric turbulence effects on a laser beam. This is because atmospheric turbulence produces distortions that tend to spread out the laser beam to increase the spot size on the target, reducing the flux to harmless levels.
Adaptive Optics SystemsAdaptive optics systems have been utilized to analyze wave front distortions in the atmosphere and modify the outgoing laser beam to compensate for the distortion so that when the beam arrives at the target the laser spot on the target is close to the same size as it would be if there was no atmospheric distortion. This is typically done with a wave front monitor and deformable mirrors. In order to measure the wave front distortions between the laser and the target a beacon in line with the target is needed. Light from this beacon is analyzed with a wave front monitor to determine the distortion. For example in some cases light from a star in line with the target may be analyzed to determine distortions. Cooperative targets can be provided with a beacon light source. However, most non cooperative targets would not provide a light source that could serve as a beacon and other in line light sources may not be available.
BACKGROUND PAPERSThe following list of references provide a good review of the technology to which the present invention relates:

 1. D. W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford University Press, 1998.
 2. M. Belen'kii and K. Hughes, Beacon Anisoplanatism, Proceeding of SPIE, Vol. 5087, 6982 (2003)
 3. M. A. Vorontsov, V. P., Sivokon, “Statistic parallelgradientdescent technique for highresolution wavefront phasedistortion correction,” J. Opt. Soc. Am., Vol. 15, pp 27452758 (1998).
 4. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Gauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am., Vol. 17, 14401453 (2000).
 5. M. A. Vorontsov, “Decoupled stochastic parallel gradient descent optimization for adaptive optics: integrated approach for wavefront sensor information fusion,” J. Opt. Soc. Am., Vol. 19, pp. 356368 (2002).
 6. M. Vorontsov and G. Carhart, “Adaptive phase distortion correction in strong specklemodulation conditions,” Optics Letters, Vol. 27 21552157 (2002).
 7. T. Weyrauch and M. A. Vorontsov, “Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications,” Appl. Opt., Vol. 44, pp. 63886401 (2005).
 8. J. C. Spall, “Multivariable stochastic optimization using a simultaneous perturbation gradient approximation,” IEEE Trans. Autom. Control, Vol. 37, pp. 332341 (1992).
 9. J. C. Spall, “An Overview of the Simultaneous Perturbation Method for Efficient Optimization,” John Hopkins APL Technical Digest, Vol. 19, Number 4, 1998.
 10. V. I. Tatarskii, Wave Propagation in a Turbulent Medium, (McGrawHill, New York, 1961).
 11. M. Belen'kii, “Tilt angular anisoplanatism and fullaperture tiltmeasurement technique using a laser guide star,” Appl. Optics, Vol. 39, 60976108 (2000).
 12. T. Goldring, and L. Carlson, “Analysis and implementation of nonKolmogorov phase screens appropriate to structured environments,” in Nonlinear Optical Beam Manipulation and High Energy Beam Propagation Through the Atmosphere, R. A. Fisher and L. E. Wilson, eds., Proc. SPIE Vol. 1060, pp. 244264, 1989.
 13. J. M. Martin, and S. M. Flatte, “Simulation of pointsource scintillation through threedimensional random media,” J. Opt. Soc. Am., Vol. 7, pp. 838847, 1990.
 14. M. Belen'kii, J. Barchers, E. Berg, D. Bruns, D. Fung, R. Gallant, C. Kirk, V. Rye, H. Runyeon, and J. Voass, “Laboratory Demonstration of Wavefront Based Stochastic Parallel Gradient Descent Adaptive Optics System,” Proceeding of SPIE, Vol. 6708, (2007).
 15. Robert J. Noll, “Zernike polynomials and atmospheric turbulence”, J. Opt. Soc. Am./Vol. 66. No. 3, March 1976.
Techniques have been proposed for using laser light reflected from the target to serve as the beacon for purposed of measuring the wave front distortions to then iteratively adapt the laser to compensate for the distortion. For example, a targetinloop (TIL) beam control approach has been developed by M. Vorontsov and others which uses an iterative optimization algorithm—Stochastic Parallel Gradient Decent (SPGD) algorithm to generate deformable mirror (DM) commands and utilizes a performance metric to provide feedback to an optimization algorithm to achieve maximum laser power density at the target. The TIL approach does not require a beacon laser, instead it provides feedback for the optimization algorithm by using the HEL return from the target. Both imagebased and specklebased performance metrics were used.
However, since light reflected from the target propagates back to the laser platform through turbulence and thermal blooming, both thermal blooming and turbulence degrade the beacon image and thus limit the sensitivity of the performance metric to the variations of the HEL beam spot size at the target. So, the imaging system may not be able to resolve small variations of the beam spot size at the target at each iteration of the optimization algorithm.
What is needed is a better approach to beam control.
SUMMARY OF THE INVENTIONThe present invention provides an improved beaconless adaptive optics system and process. A target is illuminated with a high energy laser beam of a directed energy laser. Wave front measurements are made of high energy laser beam reflections from the target. These wave front measurements are analyzed by a high speed processor to determine both high frequency phase components and low frequency phase components in the wave front data. (Applicants' experiments have shown that there is a direct correlation between beam spot size on the target and the phase variance of the reflected laser beam. The correlation is: the greater the phase variance the smaller the beam spot size.) Applicants have developed a technique for providing special control algorithms that provide very high speed control of the elements of a deformable mirror using this phase variance as a feedback parameter. Applicants have also developed algorithms to correct a limited number of Zernike modes associated with the wave front control.
A first preferred embodiment of the present invention provides a beam control approach somewhat similar to the approached pioneered by M. Vorontsov and others that is discussed in the background section of this specification. Applicants have introduced a concept of a Wavefrontbased Stochastic Parallel Gradient Decent (WSPGD) adaptive optics system, which uses offaxis wavefront measurements of laser return to provide feedback for an optimization algorithm. Applicants have validated this concept in simulation using a waveoptics code. The WSPGD adaptive optics system concept is based on three findings:

 the phase aberrations of laser return from the target contain information about beam spot size at the target;
 the variance of differential local wavefront tilt depends inversely proportional on beam spot size at the target; and
 correction of a limited number of loworder Zernike modes significantly increases onaxis intensity and power in the bucket at the target. We evaluated the performance of the WSPGD adaptive optics system in simulation for two tactical engagement scenarios.
This specification is organized as follows. Applicants first examine the effect of an extended beacon on wavefront statistics of laser return. The WSPGD adaptive optics system concept is then described along with a preferred WSPGD algorithm and its implementation. Applicants then describe wave optics simulation results for two tactical engagement scenarios.
Effect of Extended Beacon on Reflected BeamA very important discovery by Applicants is that the wavefront statistics of laser return from a spot on a target contain information about beam spot size at the target.
The above results imply that an extended beacon acts as a low pass filter, filtering out the high frequency phase aberrations of laser return. This effect makes turbulence appear less random in a wavefront sensor, thus reducing the root mean square (rms) phase aberrations. As a consequence, the phase aberrations of laser return from an extended beacon contain information about beam spot size at the target.
Also the reader should note that the rms phase difference between a point and extended beacon is close to the rms phase for a point beacon. This explains why beacon anisoplanatism degrades a phase conjugate adaptive optics system performance. A lot of high frequency phase components in a wavefront of a laser return from an extended beacon does not allow us to focus the beam to a diffraction limited spot. When the wavefront corrupted by beacon anisoplanatism is applied to an outgoing beam, a corrected beam tends to match the size of an extended beacon, but not the point source. This degrades the system performance. At the same time, these phase measurements can provide a useful signal for beam control algorithm.
A block diagram of the WSPGD adaptive optics system 2 is shown in
The system operates as follows. The wave front sensor measures wave front distortions of a laser return from the target. The beam quality metric is defined as one over the variance of the differential wavefront slopes, averaged over all the subapertures of the wave front sensor.
J(t_{n})=1/σ_{Δφ}^{2}(t_{n}) (1)
The control commands to the deformable mirror are independently varied, and the performance metric is minimized through gradient descent. The variance of the differential wavefront slopes increases as the solution for the actuator commands converges, and the beam spot diameter reduces. The reader should note that because phase measurements performed by all the subapertures of the wave front sensor are used to estimate a single quantity, the space averaged variance of the differential wavefront slopes, the space averaged variance is not sensitive to the turbulenceinduced scintillation.
Description and Implementation of WSPGD Adaptive Optics AlgorithmThe standard stochastic parallel gradient decent (SPGD) algorithm is a derivative based approach for minimization (or maximization) of a cost function. The principle operation consists of a gradient estimation based on control parameter perturbations. A local minimum of the cost function is approached by incremental adjustment of the control parameters in the direction of the negative of the gradient of this function at the current point.
An advantage of gradient descent algorithms is that the solution can be found without prior knowledge of the system or input parameters. One of the key benefits of SPGD algorithms is that minimization should occur in a timely manner, regardless of the number of control parameters used. The structure of the algorithm does not change since all control parameters are simultaneously perturbed. This requires only two perturbations per iteration of gradient assessment, decreasing the number of measurements leading to convergence.
Gradient descent algorithms operate by applying slight disturbances above and below a current state of a given function, coupled with measurements of the resulting feedback. These disturbances can be represented in Equation 2 as c_{k}Δ_{k}, where c_{k }represents a diminishing perturbation width and Δ_{k }is a random number determined by Bernoulli distribution.
{circumflex over (θ)}_{k}^{+}={circumflex over (θ)}_{k}+c_{k}Δ_{k}, {circumflex over (θ)}_{k}^{−}={circumflex over (θ)}_{k}−c_{k}Δ_{k} (2)
Based on a vector of motion, determined by the normalized difference of performance metric feedback, the gradient descent algorithm can determine the amount of motion and the desired direction to move.
The gradient is then multiplied by a diminishing gain, a_{k}, which reduces as a function of iteration number as shown in Eq. 4, where a is the initial gain applied to the system, k is the iteration number, A is a damping coefficient and α is the gain decrement factor.
The algorithm motion is determined by taking the current state and subtracting the product of Equations. 3 and 4. As k→∞, the gain a_{k}→0 and the algorithm reaches a steady state solution. The choice of gain coefficient is critical to the performance.
The implementation of the WSPGD algorithm is very similar to that of the SPGD. A uniqueness of the WSPGD algorithm implementation is associated with the use of variance of differential wavefront slopes to provide feedback to the beam control algorithm. The WSPGD algorithm maximizes the differential wavefront slope variance of laser return, which corresponds to a minimal beam spot size at the target.
In a conventional phase conjugate system, the wavefront sensor controls the deformable mirror. The number of control parameters corresponds to the number of actuators of the deformable mirror. The use of Zernike coefficients in the WSPGD implementation effectively reduces the number of free parameters from the number of deformable mirror actuators to a limited number of coefficients. The robustness of the WSPGD structure allows for multiple Zernike polynomials to be simultaneously controlled for correction of both low and high order aberrations. By controlling a limited number of relatively loworder Zernike modes (for example≦14), a vast improvement in the Strehl ratio and reduction in the beam spot size can be achieved, yielding a quicker convergence but providing sufficient compensation.
Simulation ResultsApplicants evaluated the WSPGD adaptive optics system performance in simulation using a waveoptics code. A propagation path was modeled using ten equally spaced turbulent layers. Each turbulent layer was generated as a phase screen and applied at the middle of each layer. The phase screens were generated with a white noise filtering approach, and an approach corresponding to the von Karman power spectrum
was simulated. In the power spectrum, the thickness of the layer was chosen to be Δz=0.2 km for L=2 km and Δz=2 km for L=20 km, the turbulence outer scale was L_{0}=5 m, and f was the spatial frequency with units of inverse meters. All screens were generated as 512×512 arrays with sample spacing, Δx, which varies from Δx=2 mm to Δx=3 mm. A target plane tracker was used to stabilize a lineofsight in a corrected beam. An image of a corrected beam in the target plane was used to provide an input for the tracker.
The simulation results for two tactical engagement scenarios are summarized below.
Each figure includes two sets of plots. The first set of plots characterizes the convergence of the WSPGD algorithm. It includes graphs of the full width half energy (FWHE) of the beam spot size at the target, Strehl ratio, and performance metric, each versus number of iterations, as well as a correlation graph between the performance metric and FWHE or Strehl ratio. The FWHE of the beam spot size at the target is given in centimeters. The second set of plots compares an uncorrected beam and a corrected beam using the WSPGD algorithm. This comparison is made using 2D intensity patterns at the target or 3D images at the target.
In
The following results have been developed:

 Applicants improved the targetintheloop beam control approach developed by M. Vorontsov with modifications to incorporate Applicants' recent discoveries. They introduced the concept of a WSPGD adaptive optics system, which uses offaxis wavefront measurements of laser return from the target to provide feedback for the optimization algorithm.
 The WSPGD beam control approach is based the following findings:
 i. the phase aberrations of laser return contain information about beam spot size at the target;
 ii. the variance of the differential wavefront slopes of laser return depends inverse proportionally on beam spot size at the target; and
 iii. correction of a limited number of loworder Zernike modes significantly increases both onaxis intensity and power in the bucket of an intensity pattern at the target.
 Applicants evaluated the WSPGD adaptive optics system performance in simulation using wave optics code for two tactical engagement scenarios.
 Applicants found that the WSPGD adaptive optics system can efficiently compensate the effects of turbulence, including beacon anisoplanatism in deep turbulence conditions, even when the diffraction limit exceeds the isoplanatic patch size.
 The Strehl ratio increases by a factor of 23.6 for L=2 km range, and wave propagation parameters: σ_{x}^{2}=0.6, D/r_{0}=9, θ_{B}/θ_{0}=8, θ_{D}/θ_{0}=1, and by a factor of 1.62.5 for L=20 km range, σ_{x}^{2}=1.2, θ_{B}/θ_{0}=20, θ_{D}/θ_{0}=2.6.
 The WSPGD adaptive optics system is immune to the effects of strong turbulence including beacon anisoplanatism because the WSPGD metric uses the phenomenology of turbulence to generate valid signal.
 Applicants experimentally validated our simulation results in the laboratory setup. A laboratory demonstration confirmed these predictions.
Although the invention has been described in terms of preferred embodiments, those who are skilled in the art will recognize that other modifications and improvements will therefore occur to those skilled in the art upon reading the foregoing description. The embodiment described herein is based on specific architectures but the present invention is not so limited. For example, the invention may be used as a directed energy system to destroy targets with the laser beam or it could be used at much lower energy values as a laser designator. The wave front sensor can be off axis or on axis. A variety of lasers, wave front sensors, controllers, processors and deformable mirrors can be used. So the scope of the invention should be determined by the appended claims and their legal equivalence.
Claims
1. An adaptive optics system comprising:
 A) a laser system, comprising a laser and a deformable mirror, adapted to illuminate a target with a high energy laser beam corrected for atmospheric distortion,
 B) a wave front sensor adapted to measure wave fronts of beams reflected from the target,
 C) a controller adapted to control components of the deformable mirror, and
 D) a high speed computer processor programmed with an algorithm adapted to analyze frequency components in the reflected beams measured by wave front sensor, to calculate phase variances of the reflected laser beam and to use the calculated phase variance values as feedback values to iteratively control segments of the deformable mirror in order to compensate for atmospheric distortion and to minimize laser spot sizes on the target.
2. The system as in claim 1 wherein said high speed computer processor is also programmed with an algorithm adapted to correct a limited number of Zernike modes associated with the wave front.
3. The system as in claim 1 wherein said wave front sensor is positioned off axis.
4. The system as in claim 1 wherein the laser is a high energy laser adapted to produce sufficient energy to destroy the target.
5. The system as in claim 1 wherein the system is adapted to function as a target designator.
6. A process for illuminating a target through atmospheric distortion with a high energy laser comprising the steps of:
 A) directing a high energy laser beam produced by a high energy laser system to a deformable mirror system adapted to redirect the laser beam through an atmosphere to a target,
 B) monitoring laser beams reflected from the target to determine phase variances in the reflected beams,
 C) analyzing the phase variances with a high speed computer processor programmed with an algorithm for analyzing frequency components measured by wave front sensor to calculate phase variance of the reflected laser beam and using the calculated phase variance values as feedback values to iteratively control segments of the deformable mirror in order to compensate for atmospheric distortion and to minimize laser spot sizes on the target
7. The process as in claim 6 wherein said high speed computer processor is also programmed with an algorithm for correcting a limited number of Zernike modes associated with the wave front.
Type: Application
Filed: Jun 6, 2008
Publication Date: Jan 29, 2009
Patent Grant number: 8025425
Inventor: Mikhail Belenkii (San Diego, CA)
Application Number: 12/157,014
International Classification: H01S 3/00 (20060101);